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SSS Similarity

In a triangle...

Question

In a triangle ABC, N is a point on AC such that BN ⊥ AC. If BN² = AN . NC, prove that ∠B = 90°.

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Solution

In , BN ⊥ AC.

Also,

We have to prove that .

In triangles ABN and BNC, we have

Adding above two equations, we get

So,

Hence

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